Charlot Lab · PINN × EFA · the physics gate

A certificate on every action.

A frozen, imperfect policy drives a nonlinear pendulum. A physics gate checks each proposed torque against the plant's energy certificate — does it make the energy provably contract, $\Delta V + \alpha\lVert s\rVert^2 < 0$? — and substitutes the certified action only when the policy would violate it. Same policy, same behavior, now with a per-step stability guarantee — at microseconds per step.

The capstone of Energy Is the Certificate × PINN: the energy is the computable certificate on any policy's action · companions: unified pendulum, PINN trust-meter

certificate satisfied (ΔV+α‖s‖²<0) raw policy violates the certificate gate fired — certified action substituted

certificate satisfied — raw — · gated 100% gate fires — of steps gate cost ~2 µs/step (<1 ms)

frozen policy = linear PD (imperfect on the nonlinear, saturated plant) · certificate + certified action from the verified pendulum energy

Both pendulums reach the goal — on a plant with enough authority, the raw policy usually gets there. That is the point: the gate's product is not task success, it is the guarantee. The raw policy satisfies the stability certificate on only ~⅔ of steps (its energy jumps upward — red — whenever a hallucinated or off-model action pushes the wrong way); the gate holds the certificate on 100% of steps, its energy descending monotonically, by substituting the certified action only on the steps where the policy's action would fail the check — and leaving the policy untouched otherwise (fewer, when you switch the hallucination spikes off). This is the PhysVLA pattern with a formal certificate underneath: a per-step, deterministic, microsecond physical-consistency guarantee bolted onto a black-box policy. Nano, single-seed, one plant, in simulation; the certificate is the per-step contraction proven for this basin — honest scope in the paper.